You know 1 is not a root because the sum of the coeffcients of the equation is 14, not zero.
It is fairly easy to try 3 by synthetic division (see attachment), which tells you that 3 is a root and the remaining quadratic factor is x²-3x-5. The quadratic formula tells you the roots of that factor are
... x = (-b±√(b²-4ac))/(2a) = (3±√29)/2
The appropriate choices are
... C. (3-√29)/2
... D. (3+√29)/2
... F. 3
_____
The quadratic formula tells you the solution to
... ax²+bx+c=0
is x = (-b±√(b²-4ac))/(2a)
We have a=1, b=-3, c=-5.
We can see that revolving the region formed by intersecting 3 lines, we will get 2 cones that are connected their bases.
Volume of the cone V=1/3 *πr²*h
1) small cone has r=5, and h=5
Volume small cone V1= 1/3 *π*5²*5 = 5³/3 *π
2) large cone has r=5, and h=21-6=15, h=15
Volume large cone V2= 1/3 *π*5²*15 = 5³*π
3) whole volume
5³/3 *π + 5³*π=5³π(1/3+1)=((5³*4)/3)π=(500/3)π≈166.7π≈523.6
Area
we see 2 right triangles,
Area of the triangle=1/2*b*h, where b -base, h -height
1) small one, b=5, h=5
A1=(1/2)*5*5=25/2
2)large one, b=5, h=15
A2=(1/2)*5*15=75/2
3)
whole area=A1+A2=25/2+75/2=100/2=
50
Answer:
Q1) (x+7)² = 9
x = -10, -4
Q2) (x-8)² = 144
x = -4, 20
Q3) (x-1)² = 81
x = -8, 10
Step-by-step explanation:
Q1) x² + 14x + 49 = 9
x² + 2(x)(7) + 7² = 9
(x + 7)² = 9
x + 7 = +/- sqrt(9)
x + 7 = 3
x = -4
x + 7 = -3
x = -10
Q2) x² - 16x + 64 = 144
x² - 2(x)(8) + 8² = 144
(x - 8)² = 144
x - 8 = +/- sqrt(144)
x - 8 = 12
x = 20
x - 8 = -12
x = -4
Q3) x² - 2x + 1 = 81
x² - 2(x)(1) + 1² = 81
(x - 1)² = 81
x - 1 =+/- sqrt(81)
x - 1 = 9
x = 10
x - 1 = -9
x = -8
Answer:
4. Slope of function B = -slope of function A
Step-by-step explanation:
Given:
Function A is given as:
The above equation is of the form , where represents slope of the line.
Therefore, on comparing the function A with the above standard form, er conclude that, slope of function A is -2.
Now, from the graph of function, we consider any two points on the graph and determine the slope of the line using the two points.
Let us consider the points
Now, the slope of the line passing through these two points is given as:
Therefore, slope of function B is 2.
Therefore, the correct relation between the slopes of the two functions is that the slope of function B is negative of the slope of function A.
Very handy question to know the answer to. I know of no place on the planet that does not have a tax of some sort.
The tax only applies when money changes hands. It does not apply to any discounts
So if you take the deal, the cost is
Cost of 2 pizzas = normal price - the discount.
Cost of 2 pizzas = 2*10.50 - 2.00
Cost of 2 pizzas = 21 - 2
Cost of 2 pizzas = 19.00 dollars.
Not you add on the sales tax. You can do this one of two ways, the long way or the short way.
<u>Long way</u>
Find the sales tax
Tax = % * cost
Tax = (7.5/100) * 19
Tax = 1.425 don't round yet.
Total Cost = purchase + tax
Total Cost = 19.00 + 1.425 = 20.425 Now round. This is a real problem. It depends on what you have been told to do about rounding when 5 is the last digit. I round up. So my answer would be 20.43 <<<<< Answer.
<u>Short Way</u>
Cost = (Price - discount)*(1 + %/100)
Cost = (21 - 2)*(1+ 7.5/100)
Cost = 19 * (1.075)
Cost = 20.425 = 20.43